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A287688 Triangle read by rows: T(j,k) is the number of distinct edge segment pairs in a j X k rectangular grid. 2
2, 6, 7, 10, 15, 13, 15, 21, 28, 22, 21, 28, 36, 45, 32, 28, 36, 45, 55, 66, 45, 36, 45, 55, 66, 78, 91, 59, 45, 55, 66, 78, 91, 105, 120, 76, 55, 66, 78, 91, 105, 120, 136, 153, 94, 66, 78, 91, 105, 120, 136, 153, 171, 190, 115, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 137 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This gives the number of pairs of edge segments that are distinct with respect to rotation and mirror images. Sequence is arranged so that j <= k (since 2 X 3 and 3 X 2 are equivalent grids), first by increasing j, then by increasing k: a(1) = 1 X 1 = 2, a(2) = 1 X 2 = 6, a(3) = 2 X 2 = 7, a(4) = 1 X 3 = 10.

Here j = A002260(n), k = A002024(n), and n = A000217(k-1) + j.

Where j != k, a(n) = A000217(j + k).

Where j = k, a(n) is approximately A236312(j-2); a(n) >= A236312(j-2).

LINKS

Doug Bell, Table of n, a(n) for n = 1..11325, rows n = 1..150, flattened.

EXAMPLE

Triangle begins:

   2;

   6,  7;

  10, 15, 13;

  15, 21, 28, 22;

  21, 28, 36, 45, 32;

  28, 36, 45, 55, 66, 45;

  36, 45, 55, 66, 78, 91, 59;

...

For n = 3, the a(3) = 7 pairs of edge segments for a 2 X 2 rectangular grid are:

  + - - +     + * * +  + * - +  + * - +  + * - +  + * - +  + * - +  + * - +

  |     | --\ |     |  |     *  |     |  |     |  |     |  |     |  *     |

  |     | --/ |     |  |     |  |     *  |     |  |     |  *     |  |     |

  + - - +     + - - +, + - - +, + - - +, + - * +, + * - +, + - - +, + - - +.

CROSSREFS

Cf. A002260, A002024, A000217, A236312. Distinct edge segments A287618.

Sequence in context: A047552 A287453 A287449 * A221847 A283766 A047216

Adjacent sequences:  A287685 A287686 A287687 * A287689 A287690 A287691

KEYWORD

nonn,tabl

AUTHOR

Doug Bell, May 29 2017

STATUS

approved

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Last modified February 22 10:19 EST 2020. Contains 332134 sequences. (Running on oeis4.)